PSI - Issue 12

A. Chiappa et al. / Procedia Structural Integrity 12 (2018) 353–369 Chiappa et al. / Structural Integrity Procedia 00 (2018) 000 – 000

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just before the red line, showing a similar shape of the oscillations. The signal reported by FEMAP is better centered in the expected interval and its shape is much more similar to that shown in the referenced literature. The second oscillation which appears in the figures is due to the reflection from the right-end of the plate. The numerical tests were repeated with a different spatial and temporal resolutions. The guidelines found for the bulk case were applied also for the instance of guided waves. It was found that a proportionality should hold between the spatial and the time steps. The interval reported in (1) is well balanced by the time pace given in (2) with unitary Courant number. A discretization of 20 nodes per wavelength was adopted since: i) its related time step satisfies the Nyquist criterion given in (3) ii) the area to be meshed had a small extent For the second set of numerical analyses the parameters b e = λ 2 /20 ൌ 0.0025 m, Δt = b e / c g,1 = 4.6 ൉ 10 -7 s were employed. Fig. 8 reports the monitored displacement obtained by COMSOL, APDL and FEMAP for the last introduced discretization. All the curves appear similar and the peaks are well centered in the expected interval. Tables Table 3 and Table 4 summarize the parameters of interest of the discussed analyses and the related running times.

a

b

Fig. 5. (a) Displacement over time of the impulse; (b) frequency spectrum of the impulse.

Fig. 6. Group velocity vs frequency for the 2D guided propagation problem.